It says "unauthorized to summon mount". How do I mount it? I'm level 22 and is currently doing the chocobo quest.

You need to finish the GC chocobo and gain the ability to ride one.

Indeed. Specifically, you need the Chocobo License that's granted at the very end of that quest. Then your Coeurl will be available under Mounts on your Actions & Traits window (after you use the bell in your inventory).